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<span class="kw">let </span><font color="Maroon" title="c1">c</font> be   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">aa</font>, <font color="Olive" title="b2">bb</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <br/> for <font color="Olive" title="b3">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Olive" title="b1">aa</font>,<font color="Olive" title="b2">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K3" title="SFMASTR3:func.3">FinSeqMin</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">aa</font>,<font color="Olive" title="b2">bb</font>,<font color="Maroon" title="c1">c</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">aa</font>, <font color="Maroon" title="c3">bb</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K3" title="SFMASTR3:func.3">FinSeqMin</a> <font color="Olive" title="b1">f</font>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K3" title="SFMASTR3:func.3">FinSeqMin</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span>)</span></span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">a</font> = <font color="Maroon" title="c2">aa</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">b</font> = <font color="Maroon" title="c3">bb</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">aux1</font> = 1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">aux2</font> = 2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">cv</font> = 3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">i0</font> = <font color="Maroon" title="c1">c</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c2">aa</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">i10</font> = <span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p2"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<span class="p1">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p2"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">i11</font> = <span class="p1">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p2"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">c</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">I12</font> =  <a href="scmfsa8b.html#K5" title="SCMFSA8B:func.5">if&gt;0</a> <span class="p1">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p2"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p2"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <span class="p3">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p4"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmnorm.html#K2" title="SCMNORM:func.2">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">I1B</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p4"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<span class="p3">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p4"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span></span>)</span> <a href="scmfsa6a.html#K8" title="SCMFSA6A:func.8">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p4"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">c</font></span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K5" title="SCMFSA8B:func.5">if&gt;0</a> <span class="p2">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p3"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p3"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <span class="p4">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p5"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmnorm.html#K2" title="SCMNORM:func.2">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">I1</font> =  <a href="sfmastr3.html#K2" title="SFMASTR3:func.2">for-up</a> <span class="p1">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p2"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p5"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<span class="p4">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p5"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span></span>)</span> <a href="scmfsa6a.html#K8" title="SCMFSA6A:func.8">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p5"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">c</font></span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K5" title="SCMFSA8B:func.5">if&gt;0</a> <span class="p3">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p4"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<span class="p3">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p4"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <span class="p5">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmnorm.html#K2" title="SCMNORM:func.2">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span>;<br/>
<a NAME="E1:42"/><span class="lab"><font color="Green" title="E31">A1</font></span>: 
 <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c2">aa</font></span>)</span> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="sfmastr3.html#K2" title="SFMASTR3:func.2">for-up</a> <span class="p3">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p4"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<span class="p0">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span></span>)</span> <a href="scmfsa6a.html#K8" title="SCMFSA6A:func.8">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">c</font></span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K5" title="SCMFSA8B:func.5">if&gt;0</a> <span class="p5">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<span class="p5">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <span class="p1">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p2"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmnorm.html#K2" title="SCMNORM:func.2">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" title="SF_MASTR:func.1">UsedIntLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c2">aa</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p2">(<span class="default"><a href="sfmastr3.html#K2" title="SFMASTR3:func.2">for-up</a> <span class="p3">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p4"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<span class="p0">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span></span>)</span> <a href="scmfsa6a.html#K8" title="SCMFSA6A:func.8">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">c</font></span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K5" title="SCMFSA8B:func.5">if&gt;0</a> <span class="p5">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<span class="p5">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <span class="p1">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p2"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmnorm.html#K2" title="SCMNORM:func.2">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#T33" title="SF_MASTR:th.33">SF_MASTR:33</a></span>;<br/>
<a NAME="E2:42"/><span class="lab"><font color="Green" title="E32">A2</font></span>: 
<span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><span class="p2">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p3"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<span class="p5">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span></span>)</span> <a href="scmfsa6a.html#K8" title="SCMFSA6A:func.8">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">c</font></span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K5" title="SCMFSA8B:func.5">if&gt;0</a> <span class="p4">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p5"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<span class="p4">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p5"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <span class="p0">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmnorm.html#K2" title="SCMNORM:func.2">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K2" title="SFMASTR3:func.2">for-up</a> <span class="p2">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p3"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<span class="p5">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span></span>)</span> <a href="scmfsa6a.html#K8" title="SCMFSA6A:func.8">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">c</font></span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K5" title="SCMFSA8B:func.5">if&gt;0</a> <span class="p4">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p5"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<span class="p4">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p5"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <span class="p0">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmnorm.html#K2" title="SCMNORM:func.2">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sfmastr3.html#T28" target="_self" title="SFMASTR3:th.28">Th28</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c16">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> or <font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K3" title="SFMASTR3:func.3">FinSeqMin</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span>)</span> )</span><br/>

<a NAME="E3:42"/><span class="lab"><font color="Green" title="E33">A3</font></span>: 
 <a href="sf_mastr.html#K1" title="SF_MASTR:func.1">UsedIntLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c2">aa</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">c</font>,<font color="Maroon" title="c2">aa</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#T18" title="SF_MASTR:th.18">SF_MASTR:18</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:42"/><span class="lab"><font color="Green" title="E34">A4</font></span>: 
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K3" title="SFMASTR3:func.3">FinSeqMin</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span>)</span></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:42_1"/>
( <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">aa</font> or <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">bb</font> or <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">c</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1"><span class="kw">suppose </span></a><a NAME="E1:42_1_1"/>
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">aa</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K3" title="SFMASTR3:func.3">FinSeqMin</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span>)</span></span><br/><div class="add"><a NAME="E2:42_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">c</font>,<font color="Maroon" title="c2">aa</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E3:42_1_1"/>
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K3" title="SFMASTR3:func.3">FinSeqMin</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="txt" href="#E3:42"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_2"><span class="kw">suppose </span></a><a NAME="E1:42_1_2"/>
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">bb</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K3" title="SFMASTR3:func.3">FinSeqMin</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span>)</span></span><br/><div class="add"><a NAME="E2:42_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><span class="p2">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p3"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></span>;<br/><a NAME="E3:42_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><span class="p2">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p3"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<span class="p5">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span></span>)</span> <a href="scmfsa6a.html#K8" title="SCMFSA6A:func.8">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">c</font></span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K5" title="SCMFSA8B:func.5">if&gt;0</a> <span class="p4">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p5"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<span class="p4">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p5"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <span class="p0">(<span class="default">3 <a href="sfmastr1.html#NK9" title="SFMASTR1:NK.9">-rdRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmnorm.html#K2" title="SCMNORM:func.2">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E4:42_1_2"/>
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K3" title="SFMASTR3:func.3">FinSeqMin</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_3"><span class="kw">suppose </span></a><a NAME="E1:42_1_3"/>
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K3" title="SFMASTR3:func.3">FinSeqMin</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span>)</span></span><br/><div class="add"><a NAME="E2:42_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">c</font>,<font color="Maroon" title="c2">aa</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E3:42_1_3"/>
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K3" title="SFMASTR3:func.3">FinSeqMin</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c1">c</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="txt" href="#E3:42"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
